Author:
Beck, József.
Imprint:Cambridge ; New York : Cambridge University Press, c2008.
Descriptionxiv, 732 p. : ill. ; 24 cm.
Note:pt. A. Weak win and strong draw -- ch. I. Win vs. weak win -- Illustration : every finite point set in the plane is a weak winner -- Analyzing the proof of theorem 1.1 -- Examples : tic-tac-toe games -- More examples : tic-tac-toe like games -- Games on hypergraphs, and the combinatorial chaos -- ch. II. The main result : exact solutions for infinite classes of games -- Ramsey theory and clique games -- Arithmetic progressions -- Two-dimensional arithmetic progressions -- Explaining the exact solutions : a meta-conjecture -- Potentials and the Erdos-Selfridge theorem -- Local vs. global -- Ramsey theory and hypercube tic-tac-toe -- pt. B. Basic potential technique : game-theoretic first and second moments -- ch. III. Simple applications -- Easy building via theorem 1.2 -- Games beyond Ramsey theory -- A generalization of Kaplansky's game -- ch. IV. Games and randomness -- Discrepancy games and the variance -- Biased discrepancy games : when the extension from fair to biased works! -- A simple illustration of "randomness" (I) -- A simple illustration of "randomness" (II) -- Another illustration of "randomness" in gamespt. C. Advanced weak win : game-theoretic higher moment -- ch. V. Self-improving potentials -- Motivating the probabilistic approach -- Game-theoretic second moment : application to the picker-choose game -- Weak win in the lattice games -- Game-theoretic higher moments -- Exact solution of the clique game (I) -- More applications -- Who-scores-more games -- ch. VI. What is the biased meta-conjecture, and why is it so difficult? -- Discrepancy games (I) -- Discrepancy games (II) -- Biased games (I) : biased meta-conjecture -- Biased games (II) : sacrificing the probabilistic intuition to force negativity -- Biased games (III) : sporadic results -- Biased games (IV) : more sporadic results -- pt. D. Advanced strong draw : game-theoretic independence -- ch. VII. BigGame-SmallGame decomposition -- The Hales-Jewett conjecture -- Reinforcing the Erdos-Selfridge technique (I) -- Reinforcing the Erdos-Selfridge technique (II) -- Almost disjoint hypergraphs -- Exact solution of the clique game (II)ch. VIII. Advanced decomposition -- Proof of the second ugly theorem -- Breaking the "square-root barrier" (I) -- Breaking the "square-root barrier" (II) -- Van der Waerden game and the RELARIN technique -- ch. IX. Game-theoretic lattice-numbers -- Winning planes : exact solution -- Winning lattices : exact solution -- I-can-you-can't games -- second player's moral victory -- ch. X. Conclusion -- More exact solutions and more partial results -- Miscellany (I) -- Miscellany (II) -- Concluding remarks -- Appendix A : Ramsey numbers -- Appendix B : Hales-Jewett theorem : Shelah's proof -- Appendix C : A formal treatment of positional games -- Appendix D : An informal introduction to game theory.
Bibliography Note:Includes bibliographical references.
